I saw this interesting tweet from @thephysicsgirl

But what is the difference? If you ask any person on the street, they might say there is no difference. In non-physics use, they would be correct. However, in physics we have very specific definitions for these terms. Surprisingly, not all textbooks agree on the definition of speed.

Let's start with the easy term: **velocity**. I'm pretty sure all the textbooks agree on this definition.

## Velocity and Average Velocity

I guess I should start from the beginning. There are two other important terms: position and displacement. Suppose that I have a moving object. It moves from location 1 to location 2 along the path shown below.

The position of location 1 is the vector from the origin to that point. Same for location 2 and the position vector 2. Position is a vector from the origin of your coordinate system to some particular point. If you change the location of the origin, your position vectors will change.

The displacement is the vector from location 1 to 2. This vector does NOT depend on the location of the origin. If you know the two position vectors, then the displacement vector would be:

Finally, we are ready for the definition of average velocity. When the object goes from position 1 to 2, it will take some time. I will call this time Δt. The average velocity would then be:

That's the average velocity. But what about just velocity? Technically, this would be called instantaneous velocity. This is just the limit as the time interval approaches zero. Of course that makes this a derivative with respect to time:

That's velocity. Pretty much everyone agrees on this definition.

## Speed and Average Speed

There are two common definitions of speed that are used in textbooks. I looked through a sample of books in my office and all of them fell into one of two definitions.

**Speed Definition 1:** The average speed is the distance traveled divided by the time it took to travel this distance. If I use the symbol *s* for speed (which isn't a very good choice), then I would write:

You can see the problem here. How do you calculate distance? In the picture example above, this would be the length of that dotted line path. The average velocity only depends on the starting and ending point, not the path but the speed depends on the path (in this definition). Also with this definition, the average speed is a scalar quantity and not a vector quantity.

Oh, most of the textbooks used this definition of average speed.